They seized control of the key northern city of Kunduz on Sunday, as well as Sar-e-Pul and Taloqan.
It means five regional capitals have fallen to the militants since Friday, with Kunduz being their most important gain this year.
The city is well connected to other areas, including the capital Kabul.
Violence has escalated across Afghanistan after US and other international forces began to withdraw their troops from the country, following 20 years of military operations.
